1 May 1994 Building proper behavior into mathematical models for shape memory alloys
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Abstract
Many mathematical models currently used for modeling shape memory alloy behavior in a control setting make use of an internal variable that has the interpretation of being the phase fraction of either austenite or martensite. Recently, more detailed models have been introduced that further discriminate phase species. These models seem to be pitched at the correct level for implementation in FEM based design protocols in that they are sufficiently detailed to accurately reflect much of the underlying physics, without having to track individual events at the microscale. In order for these models to enjoy reliable predictive status, it is necessary that conditions be built into them that ensure proper qualitative behavior for all processes to which the model will be applied. We discuss how the constitutive functions which enter into these models (such as the phase fraction envelope curves) can be validated to ensure proper behavior in general processes.
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Thomas J. Pence, Yefim Ivshin, "Building proper behavior into mathematical models for shape memory alloys", Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); doi: 10.1117/12.174202; https://doi.org/10.1117/12.174202
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KEYWORDS
Control systems

Mathematical modeling

Silicon

Shape memory alloys

Crystals

Thermodynamics

Information operations

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